Imposition of essential boundary conditions in the element-free galerkin method

摘要

Three methods for the imposition of essential boundary conditions in the element-free Galerkin method: (A) a coupled FEM-EFG approach, (B) the use of singular weighting functions, and (C) a new method which uses a coupled FEM-EFG approach and that employs singular weighting functions, are compared. Convergence of displacement (L_2 error norm) and displacement derivatives (energy norm) is analyzed for a series of two-dimensional numerical examples including a constant stress field patch test, a linear stress field patch test, and the bending of a cantilever beam with end loading. A comparison of solution accuracy and convergence rate for each of the three methods shows that the coupled FEM-EFG method provides the highest level of overall accuracy for the problems under consideration. However, the convergence rates for each of the three methods are similar. It is shown that the addition of the FEM coupling to method B does not significantly improve results with regards to both solution accuracy or convergence rate.